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arXiv · 1201.2550

Infinitesimal Lyapunov functions for singular flows

Vitor Araujo·Luciana Salgado
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Abstract

We present an extension of the notion of infinitesimal Lyapunov function to singular flows, and from this technique we deduce a characterization of partial/sectional hyperbolic sets. In absence of singularities, we can also characterize uniform hyperbolicity. These conditions can be expressed using the space derivative DX of the vector field X together with a field of infinitesimal Lyapunov functions only, and are reduced to checking that a certain symmetric operator is positive definite at the tangent space of every point of the trapping region.

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Vitor Araujo, Luciana Salgado. 2015-04-12. Infinitesimal Lyapunov functions for singular flows. https://doi.org/10.1007/s00209-013-1163-8

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